Abstract
In this work, we develop new data augmentation algorithms for Bayesian analysis of directional data using the von Mises-Fisher distribution in arbitrary dimensions. The approach leads to a new class of distributions, called the Modified Pólya-Gamma distribution, which we construct in detail. The proposed data augmentation strategies circumvent the need for analytic approximations to integration, numerical integration, or Metropolis-Hastings for the corresponding posterior inference. Simulations and real data examples are presented to demonstrate the applicability and to apprise the performance of the proposed procedures.
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